Description

Number Theory seminar

Tuesday, January 16, 16:00 - 17:00

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Venue: Room 105

Host: Ravi Raghunathan

Speaker: Surya Ramana

Affiliation: Harish-Chandra Research Institute

Title: An Improved Bound for the Additive Energy of Large Sets of Prime Numbers

Abstract: When A and B are subsets the integers, the additive energy of A and B is the quantity E(A,B) defined by E(A,B) = | { (x_1,x_2,y_1, y_2) \in A\times A \times B \times B\, | x_1 +y_1 = x_2 +y_2 } | Additive energy is a basic notion in additive number theory and additive combinatorics. Given $\alpha$ in $(0,1)$ and $\lambda >0$ and a large enough integer $N$, we obtain an essentially optimal upper bound for the additive energy $E(A,B)$ of any subsets $A$ and $B$ of the prime numbers in the intervals $[1, N]$ and $[1, \lambda N]$ respectively, when $A$ satisfies $|A| \geq \alpha N$. This is based on work with K. Mallesham and Gyan Prakash.

Date

Tue, January 16, 2024

Start Time

4:00pm-5:00pm IST

Duration

1 hour

Priority

5-Medium

Access

Public

Created by

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Updated

Mon, January 15, 2024 10:31am IST